Longitudinal data with a nonlinear functional form is ubiquitous in the behavioral sciences. In studies of substance abuse, trajectories of drug use over time are distinctly nonlinear. It is paramount that the nonlinearity be properly modeled. If it is not, researchers run the risk of drawing biased or misleading conclusions from an incorrect model. The proposed project will unify the disparate literature on longitudinal modeling of trajectories with nonlinear functional forms. Following a unification of the literature analytic comparisons will be made between the different methods of modeling nonlinearity. The analytic comparisons will generate testable hypotheses for an empirical evaluation of the methods in a simulation study. The proposal is organized around three specific aims. Aim 1 is to review and organize the literature in order to have an up-to-date representation of the available methods. Aim 2 is to analytically evaluate and compare the methods described by Aim 1. Aim 3 will evaluate hypotheses generated from Aim 2 in a simulation study that will empirically evaluate the performance of the different methods under four conditions: alternative functional forms of the underlying data; a range of sample size; the number of occasions of measurement; finally, the magnitude of the random effect in the parameters of the models will range from small to relatively large. It is hoped that the proposed project will make a valuable and unique contribution to the field by providing behavioral scientists with guidance for utilizing these methods and methodological researchers with directions for future extensions and research.